continuous_functions

# continuous_functions - x = → Notice this is continuity at...

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MAC 2233 Continuous Functions Section 1.6 What do we mean by continuous ? Put pencil to paper and draw a curve . .. Continuous means - you can draw the curve WITHOUT lifting your pencil from the paper What this means: The limit (the y-value the function approaches as x b a) is the SAME number as the y-value for x = a. ) ( ) ( lim a f x f a x = Therefore, we MUST have a y-value and a limit at x = a and they must be the same number. DEFINITION : A function is continuous at a point ‘ a’ if ) ( ) ( lim a f x f a

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Unformatted text preview: x = → Notice this is continuity at a single point. ONE point. If we wish to say a function is continuous over an entire interval of values, it must be continuous at each and every point in that interval. Which of the following functions are continuous at x = 1? 1. 1 3 2 ) ( 2 − − + = x x x x f 2.      = ≠ − − + = 1 4 1 1 3 2 ) ( 2 x x x x x x g 3.    > ≤ + = 1 1 3 ) ( x x x x x R 4. 1 3 ) ( − + = x x x z...
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## This note was uploaded on 10/12/2010 for the course MAC mac 2233 taught by Professor Delarosa during the Spring '10 term at Miami Dade College, Miami.

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continuous_functions - x = → Notice this is continuity at...

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